Does subdivision surface modifier and box modeling require retopology?
In general you'd want to retopo and create a low poly game model. That is for two reasons:


You want to animate the character. Since moving the character makes flaws in the topology very apparent retopo is necessary. The topology should allow natural movement of limbs and facial expressions.
For efficiency reasons you don't want to go way overboard with the vertex count. While hero props and characters may be high in details, you should only use real geometry were it's necessary. Everything that doesn't impact the actual shape can be compensated by textures, namely normal maps and PBR materials. This is done by "baking". You create a low poly model and bake the details from the high poly model into the texture.